Theories of motor control postulate that the brain uses internal models of the body to control movements accurately. Internal models are neural representations of how, for instance, the arm would respond to a neural command, given its current position and velocity. Previous studies have shown that the cerebellar cortex can acquire internal models through motor learning. Because the human cerebellum is involved in higher cognitive function as well as in motor control, we propose a coherent computational theory in which the phylogenetically newer part of the cerebellum similarly acquires internal models of objects in the external world. While human subjects learned to use a new tool (a computer mouse with a novel rotational transformation), cerebellar activity was measured by functional magnetic resonance imaging. As predicted by our theory, two types of activity were observed. One was spread over wide areas of the cerebellum and was precisely proportional to the error signal that guides the acquisition of internal models during learning. The other was confined to the area near the posterior superior fissure and remained even after learning, when the error levels had been equalized, thus probably reflecting an acquired internal model of the new tool.